Latent variable models are commonly used in psychology and increasingly used for analysing brain imaging data. Such studies typically involve a small number of participants (n <100), where standard asymptotic results often fail to control the type 1 error appropriately. The paper presents two corrections improving the control of the type 1 error of Wald tests in latent variable models estimated by using maximum likelihood. First, we derive a correction for the bias of the maximum likelihood estimator of the variance parameters. This enables us to estimate corrected standard errors for model parameters and corrected Wald statistics. Second, we use a Student t‐distribution instead of a Gaussian distribution to account for the variability of the variance estimator. The degrees of freedom of the Student t‐distributions are estimated by using a Satterthwaite approximation. A simulation study based on data from two published brain imaging studies demonstrates that combining these two corrections provides superior control of the type 1 error rate compared with the uncorrected Wald test, despite being conservative for some parameters. The methods proposed are implemented in the R package lavaSearch2, which is available from https://cran.r-project.org/web/packages/lavaSearch2.

中文翻译：

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潜在变量模型中Wald检验的小样本校正

潜变量模型通常在心理学中使用，并且越来越多地用于分析脑成像数据。此类研究通常涉及少数参与者（n <100），其中标准渐近结果通常无法适当控制1型误差。本文提出了两种更正，它们改进了通过使用最大似然估计的潜在变量模型中Wald检验的1类错误的控制。首先，我们得出方差参数的最大似然估计器的偏差的校正。这使我们能够估计模型参数和校正后的Wald统计量的校正后标准误差。其次，我们使用学生t-使用分布而不是高斯分布来说明方差估计量的变化。通过使用Satterthwaite近似来估计学生t分布的自由度。基于来自两项已发表的脑成像研究的数据的模拟研究表明，尽管对某些参数比较保守，但与未经校正的Wald检验相比，将这两种校正相结合可以更好地控制1型错误率。所提出的方法在R包lavaSearch2中实现，可从https://cran.r-project.org/web/packages/lavaSearch2获得。